Picking the most likely candidates for further development:

In the age of modern high dimensional biology, when choosing potential genomic targets and physiological pathways for future study or drug development, investigators need to select a modest number of candidates from among very large numbers of options. In prioritizing these options, they may seek potential targets that meet all of several criteria. For example, they might wish to choose genes that are differentially expressed in response to a particular stimulus in each of several model organism species (i.e. evolutionarily conserved responses), or genes that are both differentially expressed in response to a particular stimulus and which produce a predicted phenotypic response when knocked down in an RNAi experiment. Both examples involve testing whether two or more null hypotheses can both be rejected; this entails the conduct of intersection-union tests (IUTs). The most common traditional IUT rejects the union of all of k null hypotheses in favor of the intersection of all k alternative hypotheses if a legitimate test for each and every one of the separate k null hypotheses is rejected at level α. This IUT is conservative in all but several unrealistic situations. Moreover, it yields results classifiable as significant or not, but not a single quantitative pvalue. Herein, we examine an approach to frequentist testing to overcome these limitations. We then present a Bayesian approach to the problem that makes more complete and intuitive use of the data when many IUTs are being conducted as in high dimensional biology.